1. Field of the Invention
This invention relates to tomography and, more particularly, to near-field microscopy wherein an image of an object is directly reconstructed with sub-wavelength resolution.
2. Description of the Background Art
Near-field scanning optical microscopy (NSOM) is a technique to obtain images of surfaces with sub-wavelength resolution. The technique is particularly important for imaging structures where spectroscopic concerns or sample handling requirements dictate the use of lower frequency fields and yet high spatial resolution is still required. Applications range from the inspection of organic and biological samples to semiconductors. Various modalities are in practical use. Two prominent examples of such modalities are xe2x80x9cillumination mode NSOMxe2x80x9d and xe2x80x9ccollection mode NSOMxe2x80x9d. In illumination mode NSOM, a tapered fiber probe with a sub-wavelength size aperture serves as a source of illumination in the near-zone of the sample. The scattered field intensity is then measured and recorded as a function of the probe position while the probe is scanned over the sample. In collection mode NSOM, the fiber probe serves to detect the scattered field in the near-zone as the sample is illuminated by a source in the far zone.
There are certain limitations of current NSOM techniques. Despite the fact that the sample may present a complicated three-dimensional structure, NSOM produces only a two-dimensional image of the sample. Indeed, rather than being an imaging method, it is more accurate to say that NSOM maps the sub-wavelength structure of the optical near-field intensity. Under certain simplifying assumptions, such as homogeneity of the bulk optical properties of the sample, the maps produced in these experiments may be related to the sample structure. However, for the more general case in which the topography of the sample and the bulk optical properties both vary, the connection between the near-field intensity and the sample structure can be ambiguous.
To resolve this ambiguity it is desirable to solve the inverse scattering problem (ISP). The ISP may be characterized as reconstructing the three-dimensional object structure, in this case the dielectric susceptibility of the sample, from measurements of the scattered field. By solving the ISP, two main issues of the prior art are resolved, namely, the ambiguity in connecting the sample properties and the measured data is resolved, and simultaneously three-dimensional, tomographic images of the sample are obtained.
Historically, solving the ISP for other scattering modalities has greatly expanded the functionality of existing methods. For instance, pioneering analysis of X-ray diffraction made modem crystallography a reality. Another pioneering work brought medical imaging out of the era of projection radiography and into the era of computed tomography (CT). In any ISP the first step is to obtain a physically reasonable forward model for the scattering process. For instance, in CT, a geometric model of propagation, neglecting any scattering, sufficiently describes the experiment. Likewise, as scattering becomes important, the first Born approximation is a reasonable model. By considering the far-zone scattered field, one may obtain a readily soluble ISP, now generally known as diffraction tomography (DT). The crucial step in the DT solution is to obtain a linearized relationship between the sample properties and the scattered field or some simple function of the scattered field. This may be accomplished by making use of models such as the first Born or first Rytov approximations. Solutions for the non-linear ISP may be obtained as well, but in general they suffer from mathematical pathologies involving convergence.
The far-zone ISP has an inherent resolution limit imposed by the wavelength of the probe field. This limit may be traced to the fact that only the homogeneous part of the scattered field contributes to the far-zone. While in principle a higher resolution image may be obtained by mathematical extrapolation, this approach is exponentially sensitive to errors in the scattering data. However, the evanescent waves which contribute to the near-field carry the higher spatial frequency information about the scatterer. It is known that inclusion of the evanescent waves in the standard back propagation algorithm of two-dimensional DT enhances the resolving power of that method.
The sub-wavelength resolution obtained in NSOM arises because direct access to the evanescent scattered waves by probing the near-field is effected. It is this part of the scattered field on which the sub-wavelength structure of the scattering object is encoded. The NSOM ISP is thus of great interest because it obtains sub-wavelength resolved three-dimensional reconstructions. This technique, in accordance with the present invention, is referred to this as xe2x80x9cscanning near-field optical tomographyxe2x80x9d.
Representative of the art in this technological area are the following U.S. patents: (a) Fiber Optic Probe for Near Field Optical Microscopy (U.S. Pat. No. 5,485,536); (b) Method and Apparatus for Performing Near-Field Optical Microscopy (U.S. Pat. No. 5,479,024); (c) Near Field Scanning Tunneling Optical Microscope (U.S. Pat. No. 5,382,789; and (d) Near Field Optical Microscopic Examination of a Biological Specimen (U.S. Pat. No. 5,286,970).
The art is devoid of any teachings or suggestions for treating the inverse scattering problem which is applicable to the near-field case.
These shortcomings, as well as other limitations and deficiencies are obviated, in accordance with the present invention, by devising explicit inversion formulas that are applicable to near-field scanning optical tomography and which provide a direct reconstruction of a scattering potential associated with a sample being scanned.
In accordance with a broad method aspect of the present invention related to scalar waves, an image of an object is generated by: (a) probing the object with incident scalar waves; (b) detecting scattered waves from the object, wherein the scattered waves are detected in a near-field collection mode; and (c) reconstructing the tomographic image by executing a prescribed mathematical algorithm with reference to the incident scalar waves and the scattered waves to generate the tomographic image with sub-wavelength spatial resolution.
In accordance with another broad method aspect of the present invention related to scalar waves, an image of an object is generated by: (a) probing the object with incident scalar waves, wherein the incident scalar waves are generated in a near-field illumination mode; (b) detecting scattered waves from the object, wherein the scattered waves are detected in the far-field of the object; and (c) reconstructing the tomographic image by executing a prescribed mathematical algorithm with reference to the incident scalar waves and the scattered waves to generate the tomographic image with sub-wavelength spatial resolution.
In accordance with yet another broad method aspect of the present invention related to scalar waves, an image of an object is generated by: (a) probing the object with incident scalar waves, wherein the incident scalar waves are generated in a near-field illumination mode; (b) detecting scattered waves from the object, wherein the scattered waves are detected in a near-field collection mode; and (c) reconstructing the tomographic image by executing a prescribed mathematical algorithm with reference to the incident scalar waves and the scattered waves to generate the image with sub-wavelength spatial resolution.
In accordance with a broad method aspect of the present invention related to electromagnetic waves, an image of an object is generated by: (a) probing the object with incident electromagnetic waves; (b) detecting scattered waves from the object, wherein the scattered waves are detected in a near-field collection mode; and (c) reconstructing the tomographic image by executing a prescribed mathematical algorithm with reference to the incident electromagnetic waves and the scattered waves to generate the tomographic image with sub-wavelength spatial resolution.
In accordance with another broad method aspect of the present invention related to electromagnetic waves, an image of an object is generated by: (a) probing the object with incident electromagnetic waves, wherein the incident electromagnetic waves are generated in a near-field illumination mode; (b) detecting scattered waves from the object, wherein the scattered waves are detected in the far-field of the object; and (c) reconstructing the tomographic image by executing a prescribed mathematical algorithm with reference to the incident electromagnetic waves and the scattered waves to generate the tomographic image with sub-wavelength spatial resolution.
In accordance with yet another broad method aspect of the present invention related to electromagnetic waves, an image of an object is generated by: (a) probing the object with incident electromagnetic waves, wherein the incident electromagnetic waves are generated in a near-field illumination mode; (b) detecting scattered waves from the object, wherein the scattered waves are detected in a near-field collection mode; and (c) reconstructing the tomographic image by executing a prescribed mathematical algorithm with reference to the incident electromagnetic waves and the scattered waves to generate the image with sub-wavelength spatial resolution.
Broad system aspects of the present invention are commensurate with these method aspects.